Result Details

Convenient adjacencies for structuring the digital plane

ŠLAPAL, J. Convenient adjacencies for structuring the digital plane. ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE, 2015, vol. 75 (2015), no. 1, p. 69-88. ISSN: 1012-2443.

Type

journal article

Language

English

Authors

Šlapal Josef, prof. RNDr., CSc., IM (FME)

Abstract

We study graphs with the vertex set Z^2 which are subgraphs of the 8-
adjacency graph and have the property that certain natural cycles in these graphs
are Jordan curves, i.e., separate Z^2 into exactly two connected components. Of
these graphs, we determine the minimal ones and study their quotient graphs. The
results obtained are used to prove digital analogues of the Jordan curve theorem
for several graphs on Z^2. Thus, these graphs are shown to provide background
structures on the digital plane Z^2 convenient for studying digital images.

Keywords

Simple graph, quotient graph, connected set, digital plane, Jordan curve

Published

2015

Pages

69–88

Journal

ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE, vol. 75 (2015), no. 1, ISSN 1012-2443

Publisher

Springer

DOI

10.1007/s10472-013-9394-2

UT WoS

000361450200005

EID Scopus

2-s2.0-84941926544

BibTeX

@article{BUT104915,
  author="Josef {Šlapal}",
  title="Convenient adjacencies for structuring the digital plane",
  journal="ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE",
  year="2015",
  volume="75 (2015)",
  number="1",
  pages="69--88",
  doi="10.1007/s10472-013-9394-2",
  issn="1012-2443"
}

Departments

Institute of Mathematics (IM)